# Pressure change with constant volume

1. Nov 23, 2013

1. The problem statement, all variables and given/known data
Given two moles of some gas with two atoms per molecule which has energy $U=aK_{B}T$.
Assume the initial pressure is $P_{i}= 2$ Atm and the initial volume is $P_{i}= 0.001\ m^{3}$.
Now we heat it in an isochoric process to $2P_{i}$.

What would be $\Delta T$?
What would be the work required to do that?
What would be the change in the gas particles' internal energy?

2. Relevant equations
$U=aK_{B}T$
$dU=PdS-TdV$

3. The attempt at a solution
Well using the first law of thermodynamics, I got that under constant volume $dV=0$ so $\frac{dQ}{dT}=\frac{\partial U}{\partial T}$ so the entire energy that we spent on heating would be transferred into the gas.
What's a tricky to me is to formulate the change in temperature as a function of pressure because $dV=0$ so I'd really welcome a hint.

Thanks!

Last edited: Nov 23, 2013
2. Nov 23, 2013

### TSny

Oops, check that.

Can you assume the gas obeys the ideal gas law?

3. Nov 24, 2013

And yes of course it was a typo :) it's supposed to be $dU=TdS-PdV$